The comment about the "dirty little secret" was more a social comment than a comment about the martial arts. Many martial arts instructors instruct their style not only for love of the art but as their livelyhood. Many of these instructors will play-up their style as better than other styles, not because it's necessarily true, but because they need to put food on the table and offering the "best" style tends to draw more customers.
Then you consider pride, one of the biggest failings of many martial artists, and you get that much more talk about their preffered style being the "best."
In my experience, the combination of pride and livelyhood is more common amongst traditionalist than non-traditionalists.
Note that while your body may lend itself to a particular style, training only in that style will leave you with its vulnerabilities as well as its strengths; for example, aikido is primarily a style of small-joint locks and throws based on the manipulation of an enemy's momentum and center of gravity. This is very useful against irrate lay-persons and heavy hitting hard styles such as certain schools of karate and, to a certain extent, tae kwon do. It'll play rather poorly against a style like some styles of kung-fu or ninjutsu that focus on lightning quick strikes from oblique angles and have a heavy emphasis on a strong sense of balance.
I freely grant that it will be uncommon to get into a fight with another martial artist, much less one who is an advanced student of an exotic style, but it's not impossible. If it does happen, wouldn't you rather you had more than one set of techniques to rely on?
Then of course there's the fact that just as some styles work well for people of a certain body type, many styles have difficulty in dealing with people of a certain body type; for example, if your body lends itself particularly well to judo, you'll find yourself having a tough time against a person who's notably shorter than you, since it's difficult to get your center of gravity below theirs for many throws. If that person has any kind of background in a grappling style, themselves, you're going to have a serious problem on your hands.
Then, of course, there are styles that are incomplete in their own right. Most styles of western boxing and many styles of kickboxing don't teach much, if anything, about what to do in a clinch or if a fight takes you to the ground, since these styles are primarily sporting in nature and clinch and ground fighting are against the rules.
As I said, if you want to be a complete, well-rounded fighter then you need to do at least some cross-training.
Cross-training in other atheletic endeavors isn't necessarily a bad idea either, since physical fitness translates just fine. I've recently begun to supplement my fighting skills with a bit of parkour/freerunning. It's demanding and fun in a completely different way than any combat sport, but the cardio and necessity of situational awareness add to my combat capability as well.